Читать книгу Chemistry and Biology of Non-canonical Nucleic Acids - Naoki Sugimoto - Страница 54

The unfolding of the tetraplex-stranded DNAs is generally not in equilibrium (Figure 3.11a). In general, the folding process for the tetraplex is very slow relative to unfolding. Therefore, the unfolding and folding processes often show different sigmoidal curves (Figure 3.11b) [19]. Due to the hysteresis of unfolding and folding processes, the thermodynamic parameters for intermolecular tetraplex using UV melting curves are not estimated. However, the equilibrium between unfolding and folding tetraplex is adopted, and the thermodynamic parameters for tetraplex formation can be estimated by the following methods.

Figure 3.11 (a) The unfolding process for the intermolecular tetraplex. (b) Unfolding and folding behaviors for intermolecular tetraplex monitored by UV absorption.

For a folding reaction involving intermolecular and intramolecular tetraplexes (Figure 3.12) from same sequences, the general equilibrium can be written as [20]

The general expression for the equilibrium constant, K, in terms of α and n is

(3.25)

Note that this expression for the equilibrium constant for an association reaction among same sequences is not identical to the corresponding expression for different sequences. If one defines the melting temperature, T_m, as the temperature at which α = 0.5, the general expression for K shown above reduces to

(3.26)

This expression allows calculation of K at the T_m for an association reaction of any molecularity among same sequences. One also can derive a general expression for calculating the transition enthalpy for self-complementary associations. To accomplish this, one substitutes Eq. (3.26) into the van't Hoff equation (Eq. 3.27):

Figure 3.12 (a–c) Typical examples for intermolecular and intramolecular tetraplexes described with equation of nA ⇌ A_n. n indicates the number of strands.

(3.27)